bank size and efficiency in developing countries ... · for example, hughes et al. (2001) found...

Asian Economic and Financial Review, 2013, 3(5):593-613

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BANK SIZE AND EFFICIENCY IN DEVELOPING COUNTRIES:

INTERMEDIATION APPROACH VERSUS VALUE ADDED APPROACH AND

IMPACT OF NON-TRADITIONAL ACTIVITIES

Sameh Charfeddine Karray

Faculty of Tunis Assistant professor in Finance, Institute of the High Commercial Studies of Sfax University of

Sfax, Tunisia.

Jamel eddine Chichti

Faculty of Tunis Professor in the High institute of commerce of Tunis

ABSTRACT

Following the using a panel of 402 commercial banks from 15 developing countries over the period

between 2000-2003 period, we assess the effect of bank size on technical efficiency and its two

components: pure technical and scale efficiencies. We use in this study data envelopment approach

(DEA) under specifications that allow the examination of the impact on results of the choice to

measure banking activities with an intermediation or a value added approach, and of course a test

for the relevance of including non traditional activities. Results indicate that examined banks suffer

from serious problems of technical inefficiency involving a total average waste of resources that

exceeds 46% of their actually levels. This inefficiency is mainly due to pure technical inefficiency

for all size of banks except the largest banks for which we found high levels of scale inefficiency.

The conducted test results show that the models with and without non-traditional activities are

equivalent in terms of overall technical efficiency for banks of all size classes except for those of

the smallest size. However, it is proved by these tests that the choice of an intermediation or a

value added approach for measuring banking activity can significantly influence the generated

average levels of technical efficiency for all bank sizes, but scale efficiency estimates appeared to

be less sensitive to this choice.

Keywords: Size, technical efficiency, bank performance, developing countries.

INTRODUCTION

In the last two decades, a vast movement of concentration and restructuring of the banking sector

has characterized almost all developed countries and many developing countries. In this field,

Asian Economic and Financial Review

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merger operations of banks supported by economic policy makers and managers of banks have

imposed a new scale of size-based banks. They constitute a specific response to the decrease in

profitability charged by firms on traditional intermediation activities and the erosion of their charter

values induced by deregulation and increased competition from both banking and non-banking

institutions. Also, there is an obligation for banks to grow at the same rate as large companies they

are funding. But more importantly, it is expected that through these acquisitions – mergers, banks

will be able to achieve better cost structures benefiting from economies of scale and scope provided

by their size and therefore improving the efficiency of their production. Better banking sector

efficiency will have its impact on the economic well-being and social development of any country

through improved profitability, greater amounts of intermediated funds, better prices and quality of

services offered to clients and increased financial system's strength and stability.

Despite these opportunities theoretically related to the increasing of banks size and the shift

towards more concentrated structures, the empirical literature does not seem to reach a consensus in

the empirical validation attempts. Indeed, if we consider the benefits of size in terms of economies

of scale, we note that the majority of studies have led to estimated cost functions with U-shaped

profile. They are decreasing with size up to a certain value of total assets and unit costs rise beyond

this level, indicating that medium-sized banks are more scale efficient than large and small banks

(Berger et al., 1987; Noulas et al., 1990; Mester, 1992; Clark, 1996). However, more recent

literature has identified some empirical evidence on the existence of scale economies in banking.

For example, Hughes et al. (2001) found economies of scale that increase with the size of

examined banks, once their risk-taking and capital structure are controlled for in the bank

production function. Wheelock and Wilson (2009) and Feng and Serlitis (2010) highlighted the

existence of economies of scale in U.S. banks. Moreover, it is worth noting that despite the rising

importance given to the evaluation of bank efficiency and the proliferation of empirical

investigations carried out on the banking sectors of several countries, it was found by many

researches such as Berger and Humphrey (1997) and Staikouras et al. (2008), that developed

countries have received the most attention in this area and the empirical evidence is still limited for

banks belonging to developing countries. In this context, this paper provides useful empirical

evidence on the cost structure and production efficiency of commercial banks in developing

countries and on the existence of systematic difference in bank performance that is explained by

size differences. Moreover, it is noted that despite the significant development of studies

attempting to assess the efficiency and productivity in the banking industry, a major problem

remains and lets their results difficult to compare and concerns the definition of bank inputs and

outputs. Mlima and Hjalmarsson (2002) have shown that efficiency scores in the banking industry

are very sensitive to the choice of variable inputs and outputs. Thus, the proposed empirical

approach adopted in this paper will allow a comparison and discussion of results in different

approaches to measuring banking activity.


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Empirical evidence provided in the present study focusing on efficiency of commercial banks in

developing countries will allow particularly assessing the situation of banks from these countries in

the new competitive environment imposed by national and international competition. Moreover,

the decomposition of the overall efficiency of banks orientates corrective actions of banking

managers to the most important sources of inefficiency. Finally, in examining the possible

differences in production performance of banks according to their size, it is possible to determine

the size of banks associated with better performance indices and therefore guide banks managers

and policy makers towards the best strategies and policy restructuring.

The rest of the paper will be organized as follow. In the second section, we will present a review of

related literature about the relationship between size and performance in banking and the treatment

in efficiency studies of deposits and non traditional activities in the measure of banking activity.

The third section of the document will be devoted to the description of the empirical methodology

of the research. The results of its application on our data will be presented and their implications

discussed in the fourth section. Finally, we will conclude in section five.

RELATED LITERATURE

Size and Efficiency in Banking

Literature aiming to generate empirical evidence on the potential impact and significance of size on

measured efficiency of banks yields no consensus. The results are subtle and sometimes ambiguous

about the direction of the possible effect. Intuitively, we can expect a positive relationship arising

from the fact that larger banks are more able to develop technical, financial, human and material

resources enhancing their efficiency. In a reverse direction, since agency, coordination and

dysfunction problems, are more accentuated in greater firms, we can expect smaller banks to

generate inefficiency scores lower than those of larger banks. A majority of studies have led to

functions of estimated average cost with U-shaped profile. They are decreasing with size up to a

certain value of total assets and unit costs rise beyond this level, indicating that it is the medium-

sized banks that seem to have a more efficient scale than large and small banks (Berger et al., 1987;

Noulas et al., 1990; Mester, 1992; Clark, 1996). But, we notice that more recent literature has

identified some empirical evidence on the existence of economies of scale in banking. For example,

Hughes et al. (2001) found for examined banks economies of scale that increase with size, once the

risk-taking and capital structure are controlled for in the bank production function. Feng and

Serlitis (2010) and Wheelock and Wilson (2009) also highlighted the existence of economies of

scale in U.S. banks. Moreover, the study of Drake and Hall (2003) provides empirical evidence on

the existence of a strong relationship between bank size and technical efficiency and scale

efficiency in Japan. In addition, Mitchell and Onvural (1996) leads to the result of a lack of

inefficiency for large American banks retained. Miller and Noulas (1996) arrived to establish a


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significant positive correlation between the size and pure technical efficiency of banks. The largest

banks have appeared to be relatively more efficient in the study of Hasan and Marton (2003) on

Hungarian banks. A positive relationship between the size and the overall efficiency of banks was

also found for Australian banks by Sathye (2001). Also, he also has established that technical

inefficiency is more important as source of overall inefficiency than allocative component. On

Turkish banks, Isik and Hassan (2002) have arrived to similar results about the dominance of

technical inefficiency, but the relationship between size and efficiency has emerged strongly

negative.

According to Berger and Mester (1997), larger banks have shown a slightly higher efficiency than

small ones, when they considered efficiency on the cost side. But in terms of profit efficiency,

smaller banking firms appeared more efficient. All, these results indicate that when banks increase

in size, they are more able to control their costs, but it becomes difficult for them to be efficient in

creating income and generate profit. On Indian banks, Srivastava (1999) found higher average

efficiencies for medium-sized banks, followed by large banks. Small banks appeared the less

efficient, which show that relationship between size and efficiency isn't positively monotonic. In

contrast, in the study of Allen and Rai (1996), the largest banks have been marked by higher levels

of inefficiency for the majority of the 15 countries studied. Also, for a sample of banks from 11

European countries, Goldberg and Rai (1996) suggest that larger banks did not show higher

efficiencies. However, no clear relationship between estimated efficiencies and size has been

proved by Fukuyama (1993) and Altunbas et al. (2000) for Japanese banks, and by Lang and

Welzel (1996) for German cooperative banks.

Measuring Bank Activity: Are Deposits Input or Output?

A major problem arising while measuring banks' activity is about the treatment o deposits. It was

pointed out by Wykoff (1992) as follows: "When deposits are outputs, why are they so cheap?

When they are inputs, why do people provide them to banks? "(p. 12)

According to the intermediation approach, taking into account the asset transformation function, we

assume that the bank uses deposits as well as other purchased inputs to produce different categories

of bank assets such as loans and investments, measured by their monetary values. In this case, bank

costs include the interest paid on borrowed funds as additional input with operational costs (costs

of physical factors). Among studies adopting this approach, we can cite Kim (1986), Fukuyama

(1993), Zaim (1995), Vennet (1996), Bhattacharaya et al. (1997) and Chaffai (1997). Indeed. This

approach is a reduced form of modeling the banking activity which focuses exclusively on the role

of banks as financial intermediaries between depositors and final users of banking assets. From this

perspective, deposits and other liabilities, in addition to real resources (labor and capital) are

defined as inputs, while outputs include only assets such as bank loans


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However, other currents of thought (including value-added and user cost approaches) suggest that

deposits should be considered as output since they constitute elements on which the customers bear

opportunity costs and they participate in the value added creation. Indeed, according to the user

cost approach, we can determine whether a financial product is an input or an output depending on

its net contribution to banking income. If the financial performance of an asset exceeds the

opportunity cost of funds, or alternatively if the financial cost of a liability is less than the

opportunity cost, they are considered as outputs, in other cases, they are considered as inputs

(Hancock, 1985). In the value added approach, we identify the categories of bank balance sheet

(assets and liabilities) as outputs by their contribution to the value or because they are associated

with the consumption of real resources (Berger et al., 1987). Considering that banks provide two

main categories of financial services: intermediation and credit services on one hand, and care,

payment and cash on the other hand, in the value added approach, deposits are considered as input

and output at the same time. Thus, under this approach, the major categories of deposit products

(demand, savings and term deposits) and credits are considered as outputs because they are

responsible for a significant proportion of the value added. Among the studies using this approach

we find Carvallo and Kasman (2005), Sathye (2001), Dietsch and Lozano (2000) and Lozano et al.

(2002).

Non Traditional Activities of Banks

It should be noted that banks around the world have diversified away from traditional financial

intermediation activities in the off-balance sheet and fees and commissions generating activities.

Thus, it may be inappropriate to focus exclusively on traditional remunerative assets and neglect an

important part of modern banking operations. Therefore, several recent studies have included

additional output variables to capture the non-traditional activities and operations of banks. In the

literature, two types of measures were used to capture these non-traditional activities one measure

is in flow terms (the non-interest income), and other measures are expressed in terms of stocks (off-

balance sheet items in nominal or weighted for risk values). Indeed, although the off balance sheet

items are not technically paying assets, they constitute a growing source of bank income (Hakimi et

al., 2012) and should therefore be included in attempts to model the characteristics of bank costs in

order not to have a total output that is under-determined (Jagtiani and Khanthavit, 1996; Altunbas

et al., 2000; Altunbas et al., 2001). Isik and Hassan (2003) showed that the exclusion of off-

balance sheet elements from the production bank specifications led to a significant deterioration in

efficiency scores and average productivity of the entire industry. According to these authors, the

extent of bias is more pronounced among the banks most involved in nontraditional activities, for

which the deteriorating levels of efficiency is more important.

Berger and Mester (1997) consider that off-balance sheet items should be included because they are

effective substitutes for direct lending and can be a source of comparable income. Also, they


598

require similar costs to gather information for initialization and for subsequent monitoring and

control. Similarly, according to Isik and Hassan (2002), off-balance sheet items are comparable to

credits in terms of risk and income. But, since the of off-balance sheet activities are generally four

or five times greater than the balance sheet items, their inclusion in efficiency models in notional

values can cause a bias. Therefore, in many studies such as those of Akhigbe and McNulty (2003),

Berger and De Young (1997), Cuesta and Orea (2002), De Young and Hasan (1998), Drake and

Hall (2003), Hasan and Marton (2003), Lang and Welzel (1996), Resti (1997), Stiroh (2000) and

Vennet (2002), researchers used non-interest income (measured by total of revenues from net

commissions and fees, and other non-interest operating revenues), as a variable approximating for

non traditional bank operations. Moreover, Vennet (2002), Cuesta and Orea (2002) and Rogers

(1998) highly recommend the inclusion of this variable as a non-traditional banking output and

suggest that traditional specifications tend to underestimate the measured efficiency of banks.

METHODOLOGY

To measure the efficiency of commercial banks in our sample, we adopt Data Envelopment

Approach. The main advantage of this method is that it does not require a priori knowledge of the

functional form of the production function and the structure of error terms or inefficiency (Avkiran,

1999; Wheelock and Wilson, 1999; Sathye, 2001; Lozano et al., 2002; Isik and Hassan, 2003;

Obafemi, 2012). However, it has the disadvantage of not taking into account the existence of

measurement errors or data.

DEA is a nonparametric technique for measuring efficiency that is extremely flexible in modeling

the production technology of a sample in a multi-inputs and multi-outputs framework. It doesn't

impose a functional form or an error structure on data and uses linear programming to construct a

production frontier with a linear convex form. This frontier envelops the data so that no observed

point is situated on the left or below it. Thus, the DEA frontier is the set of efficient observations

ensuring that no unit or linear combination of production units can use less input to produce the

same amount of outputs, or can generate more outputs without altering the quantities of used

inputs. DEA oriented in input allows us to determine the inputs saving that can be achieved for

each unit of the sample if it was as efficient as the firm of best practices (ie located on the frontier).

Data Envelopment Analysis Approach (DEA)

Measuring efficiency by frontier estimation is due to the work of Farrell (1957) proposing to define

simple measures of firms' efficiency which take into account multiple inputs cases. DEA in its

current form was originally introduced in 1978 by Charnes, Cooper and Rhodes who proposed a

model oriented in inputs and assumes constant returns to scale. Several subsequent studies have

considered various alternative hypotheses including the assumption of variable returns to scale


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suggested by Banker et al. (1984). In the model of Charnes et al. (1978), with an inputs oriented

view, the construction of an efficiency frontier from a set of observations leads to solving a

sequence of linear programs. In fact, for each of the n firms (or observations), this program is:

zMinyxK

,),(

(1)

Subject to

Yzy .

Xzx .

z= (z1 ,z2,...,zn ) (0,0,...,0)

where y = (y1, y2, ..., yq) is the row vector of observed outputs produced by a particular firm, and x

= (x1, x2, ..., xp) is the row vector of inputs used by the firm. The (nq) matrix of observed inputs

for all firms is denoted Y. The (np) matrix of observed inputs for all firms is denoted by X. K (x,

y) indicates the overall technical efficiency of the ith

firm as measured by the obtained value of..

Here indicates the fraction by which a firm can contract its inputs while continuing to produce

outputs in quantities of at least equal to current levels. must be less than or equal to unity, with a

value of 1 indicating a firm located on the efficiency frontier and therefore is technically efficient. z

is a vector of intensity weights attached to each of the n observations. Coelli et al. (2005) suggest

that the production technology associated with the program (1) can define according to Färe et al.

(1994) a closed and convex set of production which admits constant returns to scale and strong

disposability of inputs. The alteration of the constraint on the intensity vector z can permit to build

production frontiers that satisfy various assumptions such as variable returns to scale found in the

model of Banker et al. (1984). The following linear programming problem has to be solved in the

case of variable returns to scale and leads to pure technical efficiency scores:

zMinyxT

,),(

(2)

Subject to

Yzy .

Xzx .

11

n

i

iz

z= (z1 ,z2,...,zn ) (0,0,...,0)

where T (x, y) is a measure of pure technical efficiency, other variables are defined as in equation

(1). For a given firm, if there is a difference between the efficiency score obtained with constant

returns to scale assumption and that obtained with variable returns to scale assumption, this

difference will be due to scale inefficiency of the firm. The scale efficiency is measured by the ratio


600

of linear programming problems with and without the constraint of constant returns to scale, and is

written as follows:

),(

),(),(

yxT

yxKyxS (3)

And so:

),().,(),( yxTyxSyxK (4)

The overall technical efficiency is therefore partly due to scale efficiency of and partly to pure

technical efficiency. A value of S (x, y) equal to unity would indicate scale efficiency.

Data

The sample included in this study is composed of 402 commercial banks belonging to 15

developing countries over the period 2000-2003, making a total of 1608 bank-observations. All

data used on individual banks are obtained from Bankscope, a financial database distributed by

IBCA - Bureau Van Dijk. For this sample, all monetary values are expressed in U.S. dollars and

were reduced to constant 2000 prices using the GDP deflator relative to each country as published

in The International Financial Statistics. Our sample is divided according to the average total assets

criterion in four size classes. In this subdivision, we have considered a representative number of

observations for each of the four following size classes:

Class1: Very small banks: Banks with total average assets less than 300 million U.S. dollars.

Class 2: Small banks: Banks with total average assets between $ 300 millions and $ 1.3 billions of

U.S. dollars;

Class 3: Medium sized Banks: Banks with total average assets between 1.3 billion and 5 billions of

U.S. dollars;

Class 4: Large banks: Banks with total average assets greater than 5 billions of U.S. dollars.

Table (1) provides a description of our sample's observations classified by country and size class.

All size classes are almost equally represented in our sample, which eliminates any bias in the

results from the dominance of one class by another.

Table-1. Observations by country and by size class

Size classes

Total

number of

observations

South

Africa Argentina Brazil Chili

South of

Korea

Arab Unite

Emirates India

Class 1 416 28 112 80 24 0 0 12

Class 2 424 8 44 104 12 0 28 56

Class 3 376 4 24 44 28 0 8 76


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Class 4 392 16 20 56 16 60 20 72

Total 1608 56 200 284 80 60 56 216

Size classes Indonesia Lebanon Malaysia Morocco Philippine Thailand Tunisia Turkey

Class 1 68 48 4 0 28 0 0 12

Class 2 40 40 28 0 28 8 20 8

Class 3 28 36 32 20 20 12 20 24

Class 4 8 4 40 8 4 36 0 32

Total 144 128 104 28 80 56 40 76

Source: Auteur

Selection of Input and Output Variables

Based on the analysis presented above and aiming to examine the sensibility of estimated

efficiency scores to alternative methods of measuring banking activity, this study focuses on two

major approaches: the intermediation approach and the value added approach.

Our first model (DEA-A Model) is based on the intermediation approach as proposed by Sealey

and Lindley (1977). Banks are considered as funds intermediates between savers and investors.

Banks produce intermediation services through the collection of deposits and other liabilities and

their allocation to different interest producing assets such as loans, securities and other investments.

In the DEA-A model, we use the outputs Y1: loans, Y2: other paying assets. The considered inputs

are X1: work, X2: physical capital and X3: borrowed funds. To test the value added approach, we

compare the results provided by this model with those of a second model considering deposits as a

further output in addition to all previously selected outputs (DEA- B Model). So, we retain in the

DEA-B model, in addition to the outputs already defined Y1 and Y2, the output Y3: deposits, and

as inputs X1, X2 and X3.

Moreover, in order to take into account non-traditional banking activity, two alternative models are

also tested. In these models, we include as additional output the variable Y4: non-interest income.

It is added to the basic outputs (Y1: loans and Y2: other paying assets) in the intermediation

approach (to have DEA-C model) and considering also the output Y3: deposits in the value-added

approach (to have DEA-D model). Input and output variables involved in the tested models are

described in the table (2). Their descriptive statistics are reported in table (3).

Table-2. Inputs and outputs variables

Variables Definitions

Inputs

- X1 : Work

- X2 : Capital

- X3 : Borrowed funds

- Total of labor expenses

- Total of fixed assets

- Total of deposits and other borrowed funds


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Outputs

- Y1 : Loans

- Y2 : Other paying assets

-Y3 : Deposits (in the value added approach)

- Y4 : Non-interest income

- Total of short term and medium-term loans

- Total of investments in securities and other

revenue generating bank assets.

- Total of checking accounts and time and saving

deposits

- Non-interest revenues provided from services

charges oh loans and transactions, income from

renting an fiduciary activities, commissions and

other operating income

Table-3. Descriptive statistics of inputs and outputs variables (2000-2003)*

Y1 Y2 Y3 Y4 X1 X2 X3

2000-2003

Mean 2396143 1928360 3422196 1155615 65669 92779 3089256

Median 433505 412340 688313 557502 15208 16863 818776

Standard deviation 6681665 4230920 8033991 1359381 165080 212942 6179755

Year 2000

Mean 1785726 1543991 2663400 696865 59000 77047 2534480

Median 367562 378304 567051 723025 12199 15136 699288


Year 2001

Mean 2047621 1751789 2970924 3413105 60301 85605 2740014

Median 405053 398440 689685 3644046 13332 16463 802260


Year 2002

Mean 2541399 1915267 3561994 328066 62092 95210 3050154

Median 441752 404355 679527 283820 15706 16613 767943


Year 2003

Mean 3209827 2502392 4492466 184426 81283 113256 4032376

Median 563238 514663 934233 102977 19122 19885 1020406


* Values are expressed in thousands of U.S. dollars.

RESULTS

The results were generated using the DEAP software developed by Coelli (1996). Their descriptive

statistics for the four size classes and with different DEA models constructed are shown in Table

(4). They appear successively for the three efficiency concepts used (overall technical, pure

technical and scale) for the entire study period and for each year separately. The efficiency

estimates obtained from DEA models constructed are tabulated and analyzed to identify how

efficiency scores vary with bank size and to what extinct the analyzed relations depend on

methodological choices of non-parametric specifications and the definition of inputs and outputs


603

variables. More precisely, we examine the results provided by the intermediation approach versus

those generated by the value-added approach and test for the impact of the introduction of banking

non-traditional activity.

The Overall Technical Efficiency

The results about the overall technical efficiency estimates for our sample of developing countries

banks are presented in the panel A of Table (4). Their observation can lead to the following key

findings. First, on the 2000-2003 period, the overall technical efficiency of our sample banks

generated by the built frontiers is comprised between 33% and 53,7% depending on size and

selected model. A value of one indicates an efficient use of inputs, that is to say, the current inputs

are at the minimum feasible level that lets to produce the actual outputs. So, the banks in our

sample could produce the same level of outputs with approximately 46 to 67% fewer resources

than those currently employed.

Second, we note that large banks (belonging to class 4) are the most efficient in overall technical

terms over the entire period of study and with all used models (for mean and median values). They

are followed by small banks (of class 2) and then those of medium size (of class 3). Very small

banks (of class 1) seem to have the more serious problems of technical inefficiency indicating

waste of resources between 62% and 67% of the levels currently used on the 2000-2003 period,

when non-traditional activities are not taken into account ( ie. with DEA-B and DEA-A models,

respectively). When these activities are included in the outputs, the inefficiency level of the banks

of this class is less important and is at a percentage of 56.3% with the model DEA-C and 52.4%

with the model DEA-D, which correspond respectively to 129% and 106% of the actually used

resources of a 100% efficient bank from the same sample to produce the same outputs. The analysis

of the evolution of the overall technical efficiency indicates deterioration in the average

performance of banks of our sample from one year to the other for banks of the three classes from

1to 3 in all combinations of inputs and of outputs studied, except in 2001 under the value added

approach (DEA and DEA-B-D) for banks of classes 2 and 3. The evolution of the Class 4 banks

performance over our study period seems to be less influenced by the decrease since we detect

stability of the average performance of these banks between 2000 and 2001 under the

intermediation approach, and an improvement between 2000 and 2002, under the value added

approach. The downward trend in average scores efficiency observed may reflect a reduction in

management practices over the period of study and / or it may be a consequence of the deteriorating

environmental (macroeconomic, institutional or regulatory) conditions. The last observation leads

to the recognition of best management practices in the larger sized banks compared to smaller

banks that can be also reflected through the better adaptation ability or resistance to changes of the

environment characteristics.


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Moreover, we note that the introduction of non-traditional activities as additional output has no

effect on measures of overall technical performance of banks in classes 3 and 4. This effect seems

to be obvious for the small banks (class 1 and class 2 but in lesser magnitudes). Indeed, taking into

account income from non-traditional activities in the outputs of banks in developing countries of

our sample has increased the overall average technical efficiency over the period 2000-2003 for

banks belonging to class 1 of 32 4%, with the intermediation approach and 28.2% with the value

added approach. These increases were respectively of 18.4% and 1.7% for class 2 banks and are

near to zero for larger banks. To test whether the differences observed by the introduction of non-

traditional activities are significant, we proceeded to the non parametric individual statistical test of

Wilcoxon (Table (5). The Wilcoxon test was recommended by Cooper et al. (2007) to statistically

test the differences between two groups in terms of efficiency. According to the authors, the non-

parametric statistics are appropriate in this case because "the theoretical distribution of efficiency

scores with the DEA method is generally unknown" (P. 233).

Under the intermediation approach (value-added), these tests confront for each size class, scores on

the DEA-A model (DEA-B) scores against the DEA-C model (DEA-D). The test results indicate

that the models with and without non-traditional activities are equivalent in terms of overall

technical efficiency for all size classes except for Class 1, where the differences are significant at

the 1% level. Thus, the smaller banks tend to be more involved in these non-traditional activities

relatively to the total volume of business than their competitors of larger size. This type of activity

seems to generate income for these banks whose negligence may involve technical efficiency

scores which are abnormally low.


606

Our results confirm the study of Isik and Hassan (2003), suggesting that the exclusion of non-

traditional activities may result in distortions in efficiency measures especially against banks that

are most active in this type of transactions. The same nonparametric test of Wilcoxon was

conducted to test the significance of differences between the scores obtained with the

intermediation approach and the value added approach successively without the additional output

Y4 (for non-traditional activities) and with it (Table (5). This led us to compare the scores of DEA-

A model to those of the DEA-B model (in the absence of Y4) and scores of DEA-C model to

scores of DEA-D model (in the presence of Y4). The test results indicate that the differences are

significant for all size classes at a confidence level of 1%. The improvement of overall technical

efficiency levels for all categories of banks is then considered significant, when deposits are

introduced into the banking outputs as suggested by the value added approach. Indeed, the passage

from an intermediation approach to a value-added approach has increased the average overall

technical efficiency over the entire period for classes 1 to 4, respectively of 14.8%, 16.4%, 19%

and 14.5%, in the absence of Y4. In the presence of Y4, this increase is respectively of 11.2%,

16.1%, 18.7% and 14.5% for these classes. Thus, we can say that although the choice of one

approach of measuring banking activity may alter the estimated levels of technical efficiency, it

doesn't seem that this choice would favor one class size compared to another or deepen the gaps

already identified in their performance levels.

Table-5. Tests of the impact of differences in treatment methods on efficiency estimates*

Models using intermediation

versus models using value added

approaches

Models with versus models without

the introduction of non-traditional

activities output (Y4)

Without Y4

(A/B) With Y4 (C/D)

Intermediation

approach (A/C)

Value added

approach (B/D)

Class 1

ETG 3,179

(0,002)

3,067

(0,002)

7,185

(0,000)

6,672

(0,000)

ETP 3,06

(0,002)

0,339

(0,019)

3,994

(0,000)

3,433

(0,001)

EECH 0,740

(0,459)

1,251

(0,211)

10,759

(0,000)

12,118

(0,000)

Class 2

ETG 5,517

(0,000)

5,505

(0,000)

0,883

(0,377)

0,733

(0,463)

ETP 5,224

(0,000)

3,205

(0,001)

4,114

(0,000)

2,444

(0,14)

EECH 0,581

(0,561)

5,033

(0,000)

7,433

(0,000)

2,753

(0,006)

Class 3

ETG 5,978

(0,000)

5,964)

(0,000)

0,046

(0,963)

0,026

(0,979)

ETP 4,972

(0,000)

3,218

(0,001)

3,989

(0,000)

1,962

(0,050)


607

EECH 1,006

(0,314)

4,692

(0,000)

9,424

(0,000)

6,440

(0,000)

Class 4

ETG 5,110

(0,000)

5,106

(0,000)

0,005

(0,996)

0,005

(0,996)

ETP 3,024

(0,003)

2,084

(0,037)

3,853

(0,000)

2,993

(0,003)

EECH 2,374

(0,018)

4,379

(0,000)

4,878

(0,000)

3,595

(0,000)

Source : Author's calculations * ETG, ETP and EECH indicate overall technical, pure technical and scale efficiencies, respectively.

It is provided for each test the value of the wilcoxon statistic and its significance level (between

parentheses).

The Pure Technical and Scale Efficiencies

The results for the two components of overall technical efficiency, namely pure technical efficiency

and scale efficiency are allocated respectively in panels B and C of Table (4). First, we can observe

for all study years that pure technical inefficiency is the major source of overall technical

inefficiency for all size classes of banks except for the largest ones.

More precisely, the results of all the models constructed show that developing countries examined

banks of the three size classes from one to three suffer more from lower pure technical inefficiency

than scale inefficiency. The largest banks (banks of class 4) are an exception to this general result.

Their pure technical efficiency average scores generated by the DEA-C and the DEA-D models on

the study period are respectively of 73.4% and 77% and those of scale efficiency are respectively of

65.6% and 70.9%. It should be noted that for these same banks of class 4, the results of DEA-A and

DEA-B models join the previously general observation about the dominance of pure technical

inefficiency on scale inefficiency, but the difference between the two types of inefficiency appears

to be less important for this size class banks than for banks belonging to other classes. We can thus

conclude that although the introduction of the Y4 output had no significant effect on the overall

technical efficiency scores of the largest banks, neglecting the importance of non-traditional

activities in the banking production, may involve irregularities in its decomposition into pure

technical and scale efficiencies for these banks. The introduction of the Y4 output resulted in an

improvement in pure technical efficiency average scores of all categories of banks of our sample

over the four years of study, and has reduced the scale efficiency of banks of class 2 to class 4. For

class 1 banks, taking into account the output Y4 has improved both pure technical and scale

efficiencies, which can explain the result previously observed on the significant effect of its

introduction on the overall technical efficiency. At a significance level of 5%, statistical tests

discerned in Table (5) indicate that the introduction of the Y4 output has a significant effect on pure

technical and scale efficiency scores of banks belonging to all size classes. Moreover, the choice to

measure banking activity with a value-added approach leads to pure technical and scale efficiency

scores for all sizes of banks that are superior to those generated by intermediation approach.

However, at a 1% significance level, statistical tests indicate that the established differences are not


608

significant for scale efficiency of banks belonging to class 1 (with and without the output Y4) and

also for other size classes when the output Y4 is excluded. Inversely, the improvement that affects

pure technical efficiency scores when moving from an intermediation approach to a value-added

approach is significant for all size classes if we accept a significance level of the 5%. At a level of

1%, both approaches involve average levels of pure technical efficiency which are statistically

equivalent for banks belonging to the two extreme classes (1 and 4) in the presence of Y4 in the

outputs. Thus, it seems that in models neglecting the non-traditional activities, it is the scale

efficiency that is the less sensitive to the choice of the measuring banking activity approach.

However, when these activities are considered among the outputs, this choice can have a significant

impact on the derived levels of technical efficiency for all banks sizes and those of scale efficiency

of all banks except the smallest ones.

On the other hand, the largest banks show in all considered combinations of inputs and outputs

pure technical efficiency average levels that are largely higher than banks of smaller sizes. Indeed,

with DEA-C model and under the assumption of variable returns to scale, a bank from class 4,

seems to have on the study period an average performance level that exceeds with 22 4% the class

1 bank average level. This gap is of 20.2% and 18.9% compared to banks from classes 2 and 3,

respectively. Similarly, with DEA-D model and on the entire period, the differences between the

average scores of pure technical efficiency of the class 4 banks and those of classes 1, 2 and 3 are

of 22.1%, 19.3 % and 16.9%, respectively. Thus, it appears that the pure technical efficiency is

monotonically increasing with the size of banks in developing countries, whatever the chosen

model chosen and the adopted method of measuring banking activity.

Moreover, it is noted that banks of class 2 size, seem to be the closest to the optimal scale with an

average of scale efficiency over the entire period situated between 88.6% and 97.3 % depending on

the model. The relationship between the scale inefficiency and bank size seems to be U-shaped,

with a maximum of inefficiency reached for banks belonging to class 4. These banks show

relatively poor levels of scale efficiency that are even lower than those found for very small banks

(class 1) regardless of the used model. Thus, for these banks, despite the existence of serious

problems of inefficiency related to their scale, their superior managerial practices in the use of

inputs relatively to banks in other size classes, has lead to overall technical efficiency average

scores that are the highest of the sample. For class 2 banks, since they seem to operate on a scale

that is very close to the optimal scale (constant returns to scale), we can say that the resolution of

the majority of their productive inefficiency problems can be realized through a more efficient use

of banking inputs, and therefore through the introduction of best management practices of inputs

allocation to the various outputs production. Moreover, although the smallest banks of our sample

seem to be less concerned than the biggest ones by the resources waste resulting from scale

inefficiency, the combination of this type of inefficiency with a relatively high pure technical


609

inefficiency has resulted in very low levels of overall technical efficiency levels. It should be also

noted that models without the output Y4 have resulted for class 3 banks in scale efficiency scores

that approximate an average of 90%, while for class 1 banks, they are to around 76%. When Y4 is

considered in the outputs, the average level of bank performance of class 1 finds an increase that

exceeds the 16%. Then, the class 1 will be classified in terms of scale efficiency in the second

range just after banks of class 2 and before those of class 3. We can thus conclude that the

exclusion of non-traditional activities in nonparametric models of efficiency studies on developing

countries banks may involve distortions that play particularly against the smallest banks.

CONCLUSION

By using a DEA non-parametric frontier approach on a sample of 402 commercial banks from

various developing countries, the current study investigates the relationship between bank size and

productive efficiency performance under different combinations of inputs and outputs banking. The

results show low levels of overall technical inefficiency with a recorded average maximum

approximating 54%. Overall, all specifications tested prove the existence of high technical

inefficiency in banks of developing countries, implying an average waste of resources (inputs) that

exceeds 46% of the current used levels while generating the same level of outputs. It was also

demonstrated that the principal source of the waste in the majority of these banks is constituted by

pure technical inefficiency and in smaller importance by scale inefficiency. This finding is found

for banks of all size classes except for the category of the largest banks (class 4), for which the

results indicate the highest levels of pure technical efficiency and the most serious problems of

scale inefficiency. The study showed a monotonic increasing relationship between pure technical

efficiency and size of banks in developing countries, whatever the model chosen and the adopted

approach of measuring banking activity. However, relating to scale efficiency, it is the banks of the

intermediate size (class 2) that appeared the most close to the optimal scale with an average level

over the entire period between 88.6% and 97.3% depending on the model. The relationship

between the inefficiency of scale and the size of banks seems to be U-shape with a maximum of

inefficiency reached by class 4 banks. In addition, another main contribution of our study is to

confront the efficiency scores generated by the two major approaches for measuring banking used

in literature (the intermediation approach and the value added approach of the added value), and to

test the impact on the results of the consideration of non-traditional activities among the banking

outputs.

The test results indicate that the models with and without non-traditional activities are equivalent in

terms of overall technical efficiency for banks of all size classes except for those of the smallest

size. In this regard, some works of literature, including that of Isik and Hassan (2003) have

suggested that the exclusion of non-traditional activities may result in distortions in efficiency


610

measures especially against banks that are most active in this type of transactions. We can infer that

they are the smallest banks of our sample that seem to be the most involved in the non-interest

income generating activities, which can be explained by a better specialization and/or by supply of

differentiated services to their customers. Our results also indicate that the choice of an

intermediation approach or a value added approach for measuring banking activity can significantly

influence the generated average levels of technical efficiency, but scale efficiency estimates

appeared to be less sensitive to this choice. However, it is demonstrated by our study that this

choice can participate to favor a size class compared to another or to dig already observed gaps in

their performance levels. Our data thus suggest that the examination of the relationship between

size and productive efficiency performance of banks is generally weakly affected by the adoption

of some approach to measuring banking activity.

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